Consider the differential equation

x2y'' − 9xy' + 24y = 0; x4, x6, (0, [infinity]).

Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval.

The functions satisfy the differential equation and are linearly independent since

W(x4, x6) = ≠ 0 for 0 < x < [infinity].

Form the general solution.

y =

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